Vine-distribution {vines}

Vine Distribution Functions

Description

Density evaluation, distribution function evaluation, and random number generation.

Usage

dvine(vine, u)
pvine(vine, u)
rvine(vine, n)

Arguments

vine

A Vine object.

u

Vector of the same dimension of the vine or a matrix with one column for each variable of the vine.

n

Number of observations.

Details

The implementation of the dvine function for CVine and DVine objects is based on the Algorithms 3 and 4 of (Aas et al. 2009), respectively.

The pvine function is evaluated through the numerical integration of the density function (using the cubature package). This is a computationally demanding procedure, even for small dimensions.

The implementation of the rvine function for CVine and DVine objects is based on the Algorithms 1 and 2 of (Aas et al. 2009), respectively.

Value

dnorm returns a vector with the evaluation of the density. pnorm returns a vector with the evaluation of the distribution function. rvine returns a matrix with one column for each variable of the vine and one row for each observation.

References

Aas, K. and Czado, C. and Frigessi, A. and Bakken, H. (2009) Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44, 182–198.

Bedford, T. and Cooke, R. M. (2001) Monte Carlo simulation of vine dependent random variables for applications in uncertainty analysis. In 2001 Proceedings of ESREL2001, Turin, Italy.

Bedford, T. and Cooke, R. M. (2001) Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial Intelligence 32, 245–268.

Kurowicka, D. and Cooke, R. M. (2005) Sampling algorithms for generating joint uniform distributions using the vine-copula method. In 3rd IASC World Conference on Computational Statistics & Data Analysis, Limassol, Cyprus.

Examples

dimension <- 3
copulas <- matrix(list(normalCopula(0.5), 
                       claytonCopula(2.75),
                       tCopula(0.75, df = 2), 
                       NULL),
                  ncol = dimension - 1, 
                  nrow = dimension - 1)
vine <- DVine(dimension = dimension, trees = dimension - 1,
              copulas = copulas)
dimnames(vine) <- c("A", "B", "C")

data <- rvine(vine, 1)
dvine(vine, data)
pvine(vine, data)